Affiliations: [a]
School of Mathematics and Statistics, Liupanshui Normal University, Liupanshui, Guizhou, China
| [b]
School of Mathematical Sciences, Sichuan Normal University, Chengdu, P.R. China
| [c]
School of Economics and Management, Chongqing University of Arts and Sciences, Chongqing, China
| [d]
School of Business, Sichuan Normal University, Chengdu, P.R. China
Correspondence:
[*]
Corresponding author. Qiang Cai, School of Business, Sichuan Normal University, Chengdu, 610101, P.R. China. E-mail: [email protected].
Abstract: As an improved form of fuzzy sets (FSs), spherical fuzzy sets (SFSs) could provide decision makers (DMs) with more free space to express their preference information. In this article, we first develop some Hamacher power aggregation operators under SFSs by power operators and Hamacher operators, including spherical fuzzy Hamacher power average (SFHPA) operator, spherical fuzzy Hamacher power geometric (SFHPG) operator, spherical fuzzy Hamacher power weighted average (SFHPWA) operator, spherical fuzzy Hamacher power weighted geometric (SFHPWG) operator, spherical fuzzy Hamacher power ordered weighted average (SFHPOWA) operator, spherical fuzzy Hamacher power ordered weighted geometric (SFHPOWG) operator, spherical fuzzy Hamacher power hybrid average (SFHPHA) operator and spherical fuzzy Hamacher power hybrid geometric (SFHPHG) operator. At the same time, some properties of the proposed operators are investigated, and the relationships between these operators and existing operators are discussed. Furthermore, a novel spherical fuzzy entropy measure is introduced to calculate unknown attribute weights. Then, some novel multiple attribute group decision making (MAGDM) methods are established by the proposed operators as well as entropy measure under SFSs. Lastly, the practicability of the presented methods is verified with a numerical case. Moreover, the robustness, availability and superiority for the developed methods are demonstrated via sensitivity analysis and further comparation with the existing methods.
Keywords: Spherical fuzzy sets, Hamacher operators, power operators, spherical fuzzy Hamacher power aggregation operators, entropy measure, multiple attribute group decision making
